Have you read the U.S. one?
"This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding."
The Hew Hampsire Constitution can say whatever it wants but if the passage conflicts with the U.S. Constitution then it is null and void.